Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-y &= 1 \\ 5x-7y &= 4\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-7y = -5x+4$ Divide both sides by $-7$ to isolate $y$ $y = {\dfrac{5}{7}x - \dfrac{4}{7}}$ Substitute this expression for $y$ in the first equation. $-x-({\dfrac{5}{7}x - \dfrac{4}{7}}) = 1$ $-x - \dfrac{5}{7}x + \dfrac{4}{7} = 1$ Simplify by combining terms, then solve for $x$ $-\dfrac{12}{7}x + \dfrac{4}{7} = 1$ $-\dfrac{12}{7}x = \dfrac{3}{7}$ $x = -\dfrac{1}{4}$ Substitute $-\dfrac{1}{4}$ for $x$ back into the top equation. $+ \dfrac{1}{4}-y = 1$ $\dfrac{1}{4}-y = 1$ $-y = \dfrac{3}{4}$ $y = -\dfrac{3}{4}$ The solution is $\enspace x = -\dfrac{1}{4}, \enspace y = -\dfrac{3}{4}$.